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OverviewThis work provides the first comprehensive introduction to the nonlinear theory of generalized functions (in the sense of Colombeau's construction) on differentiable manifolds. Particular emphasis is laid on a diffeomorphism invariant geometric approach to embedding the space of Schwartz distributions into algebras of generalized functions. The foundations of a 'nonlinear distributional geometry' are developed, supplying a solid base for an increasing number of applications of algebras of generalized functions to questions of a primarily geometric mature, in particular in mathematical physics. Applications of the resulting theory to symmetry group analysis of differential equations and the theory of general relativity are presented in separate chapters. These features distinguish the present volume from earlier introductory texts and monographs on the subject. Audience: The book will be of interest to graduate students as well as to researchers in functional analysis, partial differential equations, differential geometry, and mathematical physics. Full Product DetailsAuthor: M. Grosser , M. Kunzinger , Michael Oberguggenberger , R. SteinbauerPublisher: Springer Imprint: Springer Edition: Softcover reprint of the original 1st ed. 2001 Volume: 537 Dimensions: Width: 15.50cm , Height: 2.60cm , Length: 23.50cm Weight: 0.795kg ISBN: 9789048158805ISBN 10: 904815880 Pages: 505 Publication Date: 08 December 2010 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Out of stock  The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of Contents1. Colombeau’s Theory of Generalized Functions.- 2. Diffeomorphism Invariant Colombeau Theory.- 3. Generalized Functions on Manifolds.- 4. Applications to Lie Group Analysis of Differential Equations.- 5. Applications to General Relativity.- Appendices.- The Chain Rule for Higher Differentials.- References.- Author Index.- Index of Notation.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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